I wrote a card game simulation for a very simple card game. The simulation runs the game multiple times and doesn't display output except for the number of wins, losses, and win %. I ran multiple simulations of millions, 10s of millions, and even 100 million games, which took several minutes. After more than 1 million games the win % tends to cluster around 1.62%. However, the mathematical win % should be 1.8316% which was confirmed by a professor of mathematics. So I should be winning 1 of every 500 games more than I am. I've checked my code over and over including what I believe to be a good use of the random number generator and the proper way to shuffle a deck of cards.
I'm wondering if someone would be willing to write their own procedure to simulate this game and see what they get for results?
The game goes like this. Shuffle the deck. Then one by one place each card face up and call out, in order, "ace" "two" "three" ... "jack" "queen" "king". Then repeat until the end of the deck. You win only if each card does not match the called out value. For example, if you get to the 5th card and it is a "5" you lose. If you get to the 28th card and it is a 2 you lose. So, obviously, you test using the mod operator % 13. I don't want to bias another solution with a post of code, but thought someone might be interested to try it themselves and, if closer to the mathematical expectation, compare code.